A novel constitutive model for surface elasticity at finite strains suitable across compressibility spectrum
A novel constitutive model for surface elasticity at finite strains suitable across compressibility spectrum
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DOI：
10.1016/j.euromechsol.2023.104981
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发表时间：
2023-03
期刊：
影响因子：
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通讯作者：
A. Javili;B. Dortdivanlioglu
中科院分区：
文献类型：
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作者：
A. Javili;B. Dortdivanlioglu
古尔廷-默多克的表面弹性理论已被证明在预测纳米尺度材料的行为方面非常成功，这可以归因于表面与体积之比随着问题维度的减小而增加的事实。另一方面，即使在宏观尺度上，表面张力也会使软弹性固体变形，从而导致例如软丝中的弹性毛细管不稳定性让人想起流体中的高原-瑞利不稳定性。由于涉及纳米级结构和凝胶等软固体的应用越来越多，表面弹性理论在过去二十年中经历了飞速发展。尽管有大量关于该主题的文献，但大变形下的表面弹性理论本构模型并不适合捕获从完全可压缩弹性到几乎不可压缩弹性的表面行为，特别是从计算角度来看。表面自由能密度在面积保持和面积变化贡献方面的物理意义和适当分解仍有待建立。我们表明，小变形表面本构模型的直接直观的推广不能通过大变形下的简单扩展测试，并导致较低泊松比下的非物理行为。因此，该手稿的第一个贡献是引入一种新颖的分解表面自由能密度，可以在整个压缩谱范围内恢复表面弹性。本文的第二个目标是根据与所提出的表面弹性模型相关的有意义的测量，从其三维格式系统地导出弹性毛细管理论的轴对称对应物。通过使用表面弹性增强的有限元方法的数值示例来阐明和讨论该问题的各个方面。
The surface elasticity theory of Gurtin–Murdoch has proven to be remarkably successful in predicting the behavior of materials at the nano scale, which can be attributed to the fact that the surface-to-volume ratio increases as the problem dimension decreases. On the other hand, surface tension can deformsoftelastic solids even at the macro scale resulting e.g. in elastocapillary instabilities in soft filaments reminiscent of Plateau–Rayleigh instabilities in fluids. Due to the increasing number of applications involving nanoscale structures and soft solids such as gels, the surface elasticity theory has experienced a prolific growth in the past two decades. Despite the large body of literature on the subject, the constitutive models of surface elasticity theory at large deformations are not suitable to capture the surface behavior from fully compressible to nearly incompressible elasticity, especially from a computational perspective. A physically meaningful and proper decomposition of the surface free energy density in terms of area-preserving and area-varying contributions remains yet to be established. We show that an immediate and intuitive generalization of the small-deformation surface constitutive models does not pass the simple extension test at large deformations and results in unphysical behavior at lower Poisson’s ratios. Thus, the first contribution of the manuscript is to introduce a novel decomposed surface free energy density that recovers surface elasticity across the compressibility spectrum. The second objective of this paper is to formulate an axisymmetric counterpart of the elastocapillary theory methodically derived from its three-dimensional format based on meaningful measures relevant to the proposed surface elasticity model. Various aspects of the problem are elucidated and discussed through numerical examples using the finite element method enhanced with surface elasticity.